UVmap spills over onto unselected areas
Mark Seam. Select [all] vertices. UV unwrap. Then move those islands that you desire to be [not affected] off the UV Map, to the side.
Set Mapping Mode to Clipped, Not Repeat.
You can see this How do I put a stencil-like texture across a sectioned object?
Know that no matter how you UV Unwrap all vertices have a texture coordinate. Even if you can not obviously see the vertices,  they still exist.  You may have seen where some mesh models have duplicate vertices that are difficult to see.  A similar lack of obvious problem can occur with UV Maps. UV Vertices can exist in the same location and be a vicious trap for the unwary Blender user.
You can identify the UV location of a face by selecting it. You can see this How can I tell what part of the model the UV map is from? (In Blender)
UV Map data Can be built with Multiple UV Unwrap user operations.  When you select [part] not [all] of mesh to UV Unwrap ... this really means ... take the explicit command for the current selection and do not change the other locations of the unselected vertices ... and use a default location for faces if the UV Map is entirely new.  Selecting part of a mesh to unwrap does not mean ...... the unselected vertices should be unaffected by the texture.